Cyber ​​Heroes

Chapter 748
Turing machine does not specifically refer to a certain or a certain type of machine, but a concept defined in the language of mathematics. It is a tool invented to answer the ultimate question of mathematics by mathematicians in the 20th century.Its purpose is to abstract and simplify the complex mathematical activities in the human mind.

Defining a Turing machine requires seven sets.The two most important ones are "limited collection of non-empty states (State)" and "limited collection of non-empty symbols (Symbol)".The former represents "the kinds of symbols that this machine can read and write on the tape", also known as the "color number".The latter represents "the state that can appear inside the machine", and is called "state number"-it can be simply understood as "the machine can be opened in first gear and second gear".

The remaining five include "blank symbol", "initial input symbol", "initial state", "transition function set", and a special "stop state", that is, "the machine must stop after entering this state".

As long as these seven elements are present, a machine can be a Turing machine.

In fact, the great mathematician Alan Turing didn't design a machine that could actually run it when he created the concept.It would be many years before von Neumann made an engineering implementation of a Turing machine based on electricity.

For example, the abacus is divided into upper and lower sides by a beam.The two upper beads can be used to express three symbols of 0~2 through the beam or not.The five beads can be used to express the six states of 0~5 through leaning on the beam or not.The abacus can be regarded as a machine with three colors and six states.

At this time, if a mathematician writes down all the transfer functions corresponding to the three colors and six states on paper, and trains a person (or monkey) to move the abacus strictly according to the set of transfer functions, then the abacus plus the user will be It can be regarded as "a Turing machine".

Yawgmoth vaguely remembered that he and Xiang Shan had done similar research many years ago.Think of DNA as the "paper tape" of the Turing machine, the four base pairs of DNA as a "set of symbols", and amino acids as a "state", ribosomes and mRNA have a "set of transfer functions"...

The nucleus of the eukaryotic organisms on the earth may be the Turing machine in the four-color N state.

Among the many Turing machines, there is one called the "beaver machine" that is the most outrageous.

BB(n), BB means "Busy Beaver", a busy beaver.is a terminating program that finds the maximum possible output given its arguments.The simplest two-color two-state beaver machine has only two states of "on and off", and can only output "0 or 1", and will stop when it outputs 1.The two-color, two-state beaver machine can output 6 4s through 1 state transitions, so BB(2)=6.

BB(3)=21.

BB(4)=107.

Then, at present, human beings have not enumerated all the beaver Turing machines with 5 states, only know that BB(5) is either 47, 176, 870, or greater than 10 to the eleventh power.

BB(6) has been determined to be greater than 7.4*10^36537.

And in 2016, a mathematician encoded Goldbach's conjecture as a 43-state beaver machine.The coding logic is very simple, which is to verify every even number from small to large.If an even number is found that can be expressed as the sum of two prime numbers, the next even number is examined.As long as this Turing machine runs BB(43) steps and does not stop before running, then humans can conclude that it will never stop, so Goldbach's conjecture is true.

But the problem is that there are fewer than 10^80 atoms in the universe.This number is even much smaller than BB(6), let alone BB(43).

Yawgmoth marveled at how outrageous the idea was.The matter and energy in the entire universe cannot support this level of calculation.If you want to record the specific value of this number, you have to record more digits than the number of atoms in the universe on each atom in the universe.This is an incalculable value.

"But even so, the pursuit of 'infinity' is still completed in the 'finite' steps." Xiang Shan introduced it this way, "If we use a more mediocre way to exhaustively enumerate all even numbers, then The matter and energy we need are 'infinite'. Rational numbers are an infinite concept. This method can only be used when Goldbach's conjecture is false at best - that is, in the infinite, a Goldbach's A counterexample to the conjecture. But BB(43), although it is larger than the universe, is a finite number. The beaver machine completes the exploration of infinity through finite steps in finite time."

"But what's even better is that humans can find even better ways to prove Goldbach's conjecture—the final proof only consumes a little light and heat overflowing from the sun. You see, the effect of wisdom is How terrible."

The energy that feeds all mathematicians from Pythagoras to Anatoly is a tiny bit of energy released by the sun, solidified by plants, transformed by animals.Insignificant compared to the universe.

But this negligible amount of energy has solved many answers that are difficult to obtain by burning the universe.

Yawgmoth nodded.But then another problem came to mind.

——Anatole completed it in 20...a few years...

……

"Compared with 'Exhaustive Infinity', the efficiency of BB(43) is frighteningly high, isn't it? But what's even more frightening is that humans can find a more efficient path to the answer to the question." Xiang Shan raised his hand Wine glass: "To our great minds."

Yawgmoth nodded.He still remembers that the long-cherished wish of his best friend is to understand "why the power of wisdom can be so efficient".

Wisdom, for this universe, what exactly is it?
Yawgmoth felt himself rekindled.Inspired by the words of his best friend, he once again remembered his dream.

In a daze, he had already finished his meal and walked back to his research room.

"Recently, there is indeed a little..." Yawgmoth pressed his head.For him, "scientific research" is a kind of comfort zone.He seemed to have closed himself in this area for a long time, dealing with various biological researches every day, so busy that he forgot everything.This kind of thing is a drain on his mind.

Fortunately, Xiangshan was there.

But at the door of the laboratory, Ingrid stopped him.

"Hello, Yog," Ingrid said to him.

Yawgmoth felt a trance.He vaguely remembered that Ying Jia seemed to have overly respected Xiang Shan recently...but another memory told him that recently there was a popular East Asian party game called "King Game" in the company...

——Is Xiang Shan someone who knows how to play this kind of game...

——No, Inga, has she finished her meal?So fast?
"Do you remember. We, you, me, Xiangshan, your ex-wife, the research we did in the Rama project." Ingrid asked, "Think of DNA as a 'paper tape' and ribosomes as a 'magnetic head' ', mRNA is regarded as a register for storing the state of the machine. Amino acids are a set of states, and the DNA code table is temporarily regarded as an instruction table... When conducting scientific research, it is the only time you are allowed to "doubt", so remember my reminder to you first .Remember it."

　Further research shows that the consistency of ZFC proves that Nandou has been reduced to BB (748)

　　
　
(End of this chapter)